Practical Use of the

Skew-T, log-p diagram for

weather forecasting

Primer on organized

convection

Outline

Rationale and format of the skew-T, log-P diagram

Some basic derived diagnostic measures

Characterizing the potential for convection

Accounting for dynamic effect of vertical wind profile

Introductory overview to organized convection

Rationales for the diagram

See the temperature and

moisture (dew point) profiles of

the observed atmosphere (as

recorded from a radiosonde)

The diagram is, at its essence, a

visual depiction of the first law of

thermodynamics (dq=du+dw)

Can be used to derive diagnostic

quantities associated with both

dry and moist adiabatic

processes. This can be quickly

done graphically without the use

of formulas, which can be quite

complicated when atmosphere is

behaving moist adiabatically.

Some basic

thermodynamically derived

quantities

Potential Temperature: Temperature that a parcel of air would potentially

have following a dry adiabat to the reference level of 1000-mb.

Utility: Absent any phase change of water, potential temperature will be

conserved as a parcel moves vertically in the atmosphere.

Lifting condensation level: Assuming dry adiabatic rise of a parcel with

its mixing ratio conserved, defines the point at which the temperature of

the parcel = dew point temperature and RH = 100%.

Utility: Defines where (the flat) cloud base is going to occur, especially for

any cumuliform cloud. Also nominally defines the height of the planetary

boundary layer, because potential temperature and mixing ratio nearly

constant in PBL.

Wet bulb temperature: temperature a parcel of air would have if it were

cooled to saturation (100% relative humidity) by the evaporation of water

into it. Find by descending along a moist adiabat from LCL. Continue on

to 1000-mb to find wet bulb potential temperature.

Utility: Wet-bulb temperature is one of the easiest manual measures of

atmospheric moisture to calculate, via use of a sling psychrometer. Also

relates to efficiency of evaporative cooling processes (e.g. swamp cooler)

Equivalent potential temperature: follow moist adiabat upward till all

moisture is condensed out. Then descend along a dry adiabat to reference

level of 1000-mb.

Utility: Potential temperature parcel of air would have if all its moisture were

condensed out. Good as a combined metric of heat and moisture, which are

requisite conditions in the lower atmosphere for convective initiation.

Commonly used in reference to any convective processes (e.g. thundestorms,

tropical cyclones), since saturated air moves along a moist adiabat

Level of free convection (LFC): Assuming moist adiabatic rise from LCL,

defines point at which the temperature of the rising parcel > temperature of the

environment. At this point the parcel is conditionally unstable and will

spontaneously rise due to its positive buoyancy.

MUST reach this point to utilize any convective available potential energy

present in the sounding. So some sort of forced lifting mechanism to trigger

the convection on synoptic scale or mesoscale (e.g. a front, differential heating

due to terrain, sea breeze circulation, mesoscale convective vortex, etc., etc.).

Vertically integrated energy due to positive buoyancy in the cloud, calculated

from the level of free convection to the equilibrium level. Units J kg-1 = m2 s-2

= CAPE

Vertically integrated negative buoyancy in the cloud, calculated from the LCL to

LFC. Initiating updraft must overcome this barrier for spontaneous convection.

Some CIN is necessary for the most severe types of thunderstorms (e.g.

supercells).

Area of negative buoyancy = CIN

-

LCL

Convective Temperature: Temperature near the surface corresponding to a

dry adiabatic lapse rate creating by heating and upward expansion of the

boundary layer during the day. Closely matches maximum daytime

temperature.

Utility: If considering a morning sounding, the convective temperature is what

is more appropriate to consider as the surface temperature, as it will define the

maximum height of the PBL.

Convective condensation level: Estimate the average dewpoint within a well

mixed boundary layer to define PBL-averaged mixing ratio. The intersection of

the modified value of w and dry adiabat from the surface convective

temperature.

Utility: Most accurate metric for cloud base height and height of the PBL during

the day. BUT…its dependent on the particular forecaster!

Diagnosing potential for

convection from CAPE and

other indices

LOTS of potential indices…we’ll

just focus on most commonly

used ones.

Which one of

these do you

use???

Whatever one you

choose, I suggest

look at CAPE and

CIN first.

Those are the

most fundamental

metrics which have

most firm basis in

physics (my

opinion).

No one “right” answer on indices…frankly depends on the preference of the

forecaster. Lots of indices because there’s a lot of regional, seasonal

dependencies on how they perform.

Bluestein, Vol 2

Moderate to strong convection = CAPE of 1000 to 3000 J kg-1

Yields a maximum vertical velocity of 70 ms-1 for CAPE = 2500 J kg-1.

Close to what is actually observed!

Showalter Index

1. From 850-mb temperature,

draw line parallel to dry

adiabats upward to LCL

2. From LCL draw line parallel to

moist adiabat upward to 500-

mb. Call this value T’

3. Subtract T’ from 500-mb

environmental T to define

index.

Not very good for high based convection, when source air for convective

clouds is above 850-mb

Lifted Index

Temperature excess at 500-mb of the environment, with respect to an air parcel

in the PBL lifted to LCL and then lifted moist adiabatically to 500-mb

Similar to the idea of the convective temperature, need to forecast PBL

characteristics in the afternoon from the morning sounding. Similar to

Showalter index but more regionally adaptable.

“K” index

K = 850-mb temperature – 500-mb temperature

+ 850-mb dew point – 700-mb dew point depression

Designed to capture the potential instability in the lower half of the atmosphere,

availability of moisture in PBL, and reduction in buoyancy through dry air

entrainment. Useful in the absence of strong synoptic-scale forcing.

Totals-Totals (TT) Index

TT= Sum of Vertical Totals (VT) and Cross Totals (CT)

VT = 850-mb temperature minus 500-mb temperature

lapse rate between two pressure surfaces

CT = 850-mb dew point minus 500-mb temperature

Combines measure of low-level moisture with temperature aloft

Does NOT involve the use of any dry or moist adiabatic lapse rates

How deep convection is depends on how far

up the instability goes in the atmosphere

Cumulus humilis Cumulus congestus Cumulonimbus

Conditionally unstable in

a shallow layer

Conditionally unstable

about midway through

troposphere

Conditionally unstable nearly

to the tropopause

Air mass

Thunderstorm

Cumulus Stage

A parcel of air is lifted from surface (updraft)

As the parcel rises, it reaches the lifting

condensation level and forms a cumulus cloud. Air

continues to rise because condensation occurs.

Lifting mechanisms include:

Mountain-valley circulations

Sea-breeze front

Thermals arising from the land surface.

Air mass

Thunderstorm

Mature Stage

Cumulonimbus with anvil.

Cloud liquid and ice particles grow

larger, eventually falling to the

ground as rain.

Process draws in drier air

surrounding the could to create a

downdraft.

Leading edge of the downdraft is

called the gust front.

Mature air mass thunderstorm

with gust front

Gust front can provide a lifting mechanism to get other storms going.

Monsoon Thunderstorms in Arizona

Forced by the diurnal

mountain valley circulation

Form over the mountains

during late morning to early

afternoon

Reach mature stage by

about mid-afternoon.

(Photo taken around 3pm)

Monsoon thunderstorms at Kitt Peak at mature

stage with gust fronts.

Air mass

Thunderstorm

Dissipating Stage

Gust front moves far enough

away from the storm to “choke off”

the updraft.

Once this supply of warm, moist

air is from the updraft is cut off,

the storm begins to weaken either

by evaporation and/or by raining

itself out.

DO

WN

DR

AF

TD

OW

ND

RA

FT

Incorporation of vertical wind

profile in diagnosing potential

for convection

Idea: In addition to thermodynamic instability

(CAPE), wind changing speed and direction with

height to facilitate convective organization.

Why that is we’ll talk about later, by further analysis

of how the shear affects growth from a dynamical

standpoint, but point is to become familiar with basic

convective types, structures now.

Why is wind shear a necessary

ingredient for severe thunderstorms?

CUMULUS STAGE

Updraft only

MATURE STAGE

Updraft + downdraft

NO WIND

SHEAR

WITH

WIND

SHEAR

(Bluestein)

Wind shear allows the updraft to be maintained in the cloud and not get

choked off by the downdraft—so the thunderstorm keeps receiving the warm,

moist air it needs to keep growing.

MOST MOST

FAVORABLE FAVORABLE

FOR GROWTHFOR GROWTH

Multicell Thunderstorms

In moderate shear, thunderstorms can get a bit more organized,

numerous and have longer lifetimes.

Note the tilted structure of the anvil with respect to the cloud base—

this indicates wind shear.

Squall Line Line of thunderstorms that

can be hundreds of miles

long.

Form along the cold front or

ahead of it in the warm

sector

Heavy precipitation on the

leading edge and then light

rain behind.

Multiple lines may form, with

the leading line being the

most severe.

Squall lines on radar image in the warm

sector of Colorado low.

(February 2007 Case)

TXTX

ARAR

LALA

Idealized squall line

thunderstorm structure

Shelf cloud at leading edge of squall line

Note the wind shear profile

Mesoscale Convective System (MCS)

A number of individual

thunderstorms cluster together

to form a giant circular

convective weather system.

Can be the size of an entire

state!

Most common in summer,

originating from convection

which forms over mountains

(the Rockies in the case of

U.S.)

Idealized structure of a mature

mesoscale convective system

Houze (1993)

Bow echoes are typically

found in well developed

mesoscale convective

complexes.

These produces very strong

(straight line) winds which can

potentially exceed hurricane

force

(75 mph).

Called a derecho

(Spanish = straight ahead)

Derecho or Straight Line Wind

Ingredients for a supercell

INGREDIENT 1: HIGH “CAPE”

Make the atmosphere more conditionally unstable by:

Warming and moistening near the surface

Cooling and drying aloft

INGREDIENT 2: LARGE HELICITY

Helicity is essentially the wind shear, or change in horizontal wind speed

and direction, through a vertical depth.

NECESSARY FOR THE STORM TO ROTATE!

(NEW) INGREDIENT 3: A CAPPING INVERSION

An inversion that occurs near about 800-mb. Only a few strong updrafts

break through the cap and utilize the enormous amount of convective

available potential energy

Tornadoes occur where three

different air masses clash

Tornadoes (and the supercell thunderstorms that spawn them) are most

prevalent in “tornado alley” in the central U.S.

Some of the most severe weather on Earth!

WARM WARM

AND DRY AND DRY

AIRAIR

(cT)(cT)

COLD AND DRY AIRCOLD AND DRY AIR

(cP)(cP)

WARM WARM

AND AND

MOIST AIRMOIST AIR

(mT)(mT)

Tornado Alley: A unique clash of air

masses like no where else on Earth

AIRMASS WINDS CHARACTER

cP Westerly

above about

700 mb

Cold and dry.

cT Southwesterly

at about

800 mb

Warm and dry.

WHAT IT DOES

CREATES

INSTABILITY

ALOFT

PROVIDES

CAPPING

INVERSION

mT Southerly to

Southeasterly

near surface

Warm and moist CREATES INSTABILITY

NEAR SURFACE AND

PROVIDES FUEL FOR

STORMS

THE “LOADED GUN” SOUNDING

THE SIGNATURE FOR SUPERCELLS!

WARM AND MOISTWARM AND MOIST

NEAR SURFACENEAR SURFACE

COOL AND COOL AND

DRY ALOFTDRY ALOFT

CAPPING

INVERSION

WIND

DRASTICALLY

CHANGES IN

SPEED

AND DIRECTION

WITH HEIGHT

Supercells on radar

NOT big long

squall lines!

Get compact and

isolated rotating

cells!

KANSAS

OKLAHOMA

TEXAS

Horizontal structure of a tornadic

supercell

TORNADOTORNADO

The tornado is located in front of the precipitation “hook” which defines the

area of hail and rain curving around the mesocyclone.

Precipitation

“hook”

Formation of a rotating

updraft in a supercell

Wind shear caused by a change in wind speed and direction with height

causes rotation in the horizontal.

Updraft in a thunderstorm tilts horizontal rotation into vertical rotation.

Net result is a relatively small, supercell rotating about a mesocyclone.

Vertical structure of tornadic supercell

REAR FLANK DOWNDRAFT: Downdraft at the base of the supercell, right

before the wall cloud.

UPDRAFT: Tornado forms at the base of the updraft is the extension of the

mesocyclone, defined by a wall cloud.

FORWARD FLANK DOWNDRAFT: Precipitation falls in the form of (possibly

large) hail and heavy rain.

UPDRAFT UPDRAFT

FORWARD FLANKFORWARD FLANK

DOWNDRAFT DOWNDRAFT

REAR FLANKREAR FLANK

DOWNDRAFT DOWNDRAFT

NOTE

WIND

SHEAR

Radar signature of a tornadic supercell

Reflectivity

TORNADOTORNADO

HOOK HOOK

ECHOECHO

FORWARD FLANKFORWARD FLANK

DOWNDRAFTDOWNDRAFT

Radar signature of a tornadic supercell

Wind velocity

YELLOW = ECHOES YELLOW = ECHOES

TRAVELING AWAY FROM TRAVELING AWAY FROM

RADARRADAR

BLUE = ECHOES TRAVELING BLUE = ECHOES TRAVELING

TOWARD RADARTOWARD RADAR

RAPID CYCLONICRAPID CYCLONIC

ROTATIONROTATION

NOTE: In Northern Hemisphere,

tornadic supercells typically rotate

counterclockwise due to the

typical wind shear profile.

They can also rotate clockwise on

rare occasions—since the vortex

is in cyclostrophic balance.

Bulk Richardson number (R)

Since storm strength is dependent on BOTH instability and shear,

can define a bulk Richardson number (R).

R = CAPE/S2

S2 = ½ (u6km – u500m)2

This measure gives some indication of the potential for organized

convection.

Supercell (tornadic) thunderstorms tend to form with 10 < R <40.

So need some sort of optimal balance of CAPE vs. shear to get

most intense kinds of thunderstorms.

RE

FLE

CT

IVIT

Y

WHICH RADAR IMAGERY INDICATES THE MOST DANGEROUS

THUNDERSTORM?

CHOOSE E IF YOU THINK THEY’RE ALL EQUALLY DANGEROUS.

A B

C D

Sounding for Alabama tornado

outbreak in late April 2011

http://www.srh.noaa.gov/images/bmx/significant_events/2011/042711/Radar/ref_80.gif